777edo

← 776edo

777edo

778edo →

Prime factorization	3 × 7 × 37
Step size	1.5444 ¢
Fifth	455\777 (702.703 ¢) (→ 65\111)
Semitones (A1:m2)	77:56 (118.9 ¢ : 86.49 ¢)
Dual sharp fifth	455\777 (702.703 ¢) (→ 65\111)
Dual flat fifth	454\777 (701.158 ¢)
Dual major 2nd	132\777 (203.861 ¢) (→ 44\259)
Consistency limit	3
Distinct consistency limit	3

The 777 equal divisions of the octave, or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.

Theory

777edo is a dual fifths system with a consistency limit of only 3.

If the harmonic 3 is excluded, it is an excellent 2.5.7.9.11.13 subgroup tuning, with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the landscape comma in the 2.9.5.7 subgroup.

Approximation of odd harmonics in 777edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.748	-0.213	-0.486	-0.049	+0.033	-0.373	+0.534	+0.064	+0.556	+0.262	+0.297
	Relative (%)	+48.4	-13.8	-31.5	-3.2	+2.2	-24.2	+34.6	+4.1	+36.0	+16.9	+19.2
Steps (reduced)		1232 (455)	1804 (250)	2181 (627)	2463 (132)	2688 (357)	2875 (544)	3036 (705)	3176 (68)	3301 (193)	3413 (305)	3515 (407)